The non-commutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary wotclosed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is us...

We show that for any C∗-algebra A, a sufficiently large Hilbert space H and a unit vector ξ ∈ H, the natural application rep(A:H) θξ −−→ Q(A), π 7→ 〈π(−)ξ, ξ〉 is a topological quotient, where rep(A:H) is the space of representations on H and Q(A) the set of quasi-states, i.e. positive linear functionals with norm at most 1. This quotient might be a useful tool in the representation theory of C∗...

We generalize the well-known numerical criterion for projective spaces by Cho, Miyaoka and Shepherd-Barron to varieties with at worst quotient singularities. Let X be a normal projective variety of dimension n ≥ 3 with at most quotient singularities. Our result asserts that if C · (−KX) ≥ n + 1 for every curve C ⊂ X, then X ∼= P .

where D−y is the Liouville right-sided fractional derivative of order a Î (0,1) of y and h >0 is a quotient of odd positive integers. We establish some oscillation criteria for the equation by using a generalized Riccati transformation technique and an inequality. Examples are shown to illustrate our main results. To the best of author’s knowledge, nothing is known regarding the oscillatory beh...

We study the computational power of pure insertion grammars. We show that pure insertion grammars of weight 3 can characterize all recursively enumerable languages. This is achieved by either applying an inverse morphism and a weak coding, or a left (right) quotient with a regular language. A consequences for the closure properties of insertion grammars are shown. We also study an application i...

The left hand side (or A–side) of this identity was a generating series for the numbers n(d) of rational curves of various degrees d lying on a smooth quintic hypersurface in P. The right hand side (B–side) was a certain hypergeometric function. The Mirror Identity states that the two functions become identical after an explicit change of variables which is defined as a quotient of two hypergeo...

Let sij represent a transposition in Sn. A polynomial P in Q[Xn] is said to be m-quasiinvariant with respect to Sn if (xi − xj) 2m+1 divides (1 − sij)P for all 1 ≤ i, j ≤ n. We call the ring of m-quasiinvariants, QIm[Xn]. We describe a method for constructing a basis for the quotient QIm[X3]/(e1, e2, e3). This leads to the evaluation of certain binomial determinants that are interesting in thei...

The paper addresses two problems belonging to the basic combinatorics of words. They are connected with the operations of sequential insertion and deletion, which are nondeterministic versions of catenation and right/ left quotient. Necessary and sufficient conditions, under which the result of sequential insertion or deletion of two words is a singleton set, are given. Also the situation when ...

In this paper, we grasp an inverse eigenvalue problem which constructs a tridiagonal matrix with specified multiple eigenvalues, from the viewpoint of the quotient difference (qd) recursion formula. We also prove that the characteristic and the minimal polynomials of a constructed tridiagonal matrix are equal to each other. As an application of the qd formula, we present a procedure for getting...

An extension of a group A by a group G is thought of here simply as a group H containing A as a normal subgroup with quotient H/A isomorphic to G. It is called a central Frattini extension if A is contained in the intersection of the centre and the Frattini subgroup of H . The result of the paper is that, given a finite abelian A and finite G, there exists a central Frattini extension of A by G...